用有限元素分析法計算溝槽表面造成的液晶表面定向強度

Abstract

本論文使用Berreman的模型，以有限元素分析法計算具有溝槽結構表面對液晶之錨定能強度。我們假設表面錨定能是由於分子的變形能所造成，以求得表面錨定能分別與溝槽深度、週期以及斜角之關係。我們發現錨定能隨著斜角呈平方的變化。而在一定的深度和斜角下，存在一個臨界週期，大於這個週期，錨定能和線密度(週期倒數)成正比。小於這個週期，錨定能則會急遽的變大。把臨界週期和相對應的深度作圖發現成線性的關係。當改變深度時，在小週期時，錨定能隨深度增加率為常數; 而在大週期時，則錨定能隨深度增加率會逐漸變小。本論文最後把我的模擬結果與現有的實驗值作比較。

With Berreman’s topological alignment model, the azimuthal anchoring strength base on finite element method was calculated. We attribute the surface anchoring strength to the elastic distortion of the liquid crystal induced by the grooves, and find the azimuthal anchoring strength in relation to depth, period, and tilt angle of the grooves. It is found that the anchoring strength is proportional to square of the tilt angle. There exists a critical period, when we fixed tilt angle and depth. Above the critical period, the azimuthal anchoring is direct proportion to the line density (inverse of the period), but anchoring strength is nonlinear increase with line density below the critical period. The critical period versus depth is linear. Changing the depth, we found the growth rate of anchoring strength to depth is constant when the period is small, but the growth rate is decrease with depth when the period is large. In the end, the simulation results are compared with the experimental data.